In the figure,if $TP$ and $TQ$ are the two tangents to a circle with centre $O$ such that $\angle POQ = 110^{\circ}$,then $\angle PTQ$ is equal to: (in $^{\circ}$)

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

$A$ tangent line drawn from a point $A$ outside $\odot(P, 5)$ touches the circle at $B.$ If $PA = 13$,then $AB = \dots$

In $\Delta ABC$,if $AB = 7, BC = 24, AC = 25$,then the diameter of a circle touching all the three sides of the triangle is ............

Write 'True' or 'False' and give reasons for your answer.
If a number of circles touch a given line segment $PQ$ at a point $A$,then their centres lie on the perpendicular bisector of $PQ$.

$PQ$ is a chord of length $8 \, cm$ of a circle of radius $5 \, cm$. The tangents at $P$ and $Q$ intersect at a point $T$ (see figure). Find the length $TP$.